If you intend to create a Pages structured blog resembling a static website as opposed to a conventional post based blog then perhaps the date can be hidden via CSS editing. However, I have no CSS skills and don't know if it can be or not.

If you have CSS editing experience, you can get the paid custom CSS upgrade and renew it annually. It will allow you to stylize the appearance of themes you find here > Appearance > Themes, but it does not allow you to change the functionality, by editing the underlying template. Also note that CSS is theme specific, so you cannot use the CSS stylesheets from other themes with the themes here at wordpress.COM.

Since there is no official Staff support for the CSS upgrade, and precious little Volunteer support, I recommend that you don’t buy the upgrade unless you have at least moderate understanding of HTML and CSS because you must be prepared to do the work on your own.

If you are considering purchasing the upgrade, you can go to Appearance > Edit CSS. There wordpress has provided a preview function where you can try before you buy.

If you do want to preview your blog without the meta-data like the date you should copy the code below into the CSS editor and make sure it is added to the existing stylesheet. This will only work for the blog linked to by your username as not all themes are designed the same. If you want the change to be permanent you will have to buy and renew the CSS upgrade as mentioned above.